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R. Bezrukavnikov and V. Ginzburg, {\em Hilbert schemes and reductive groups}, in preparation.



J. Fogarty, {\em Algebraic families on an algebraic surface}, Amer. J. Math. {\bf 90} (1968) 511--521.


I.~B. Frenkel and V.~G. Kac, {\em Basic representations of affine Lie algebras and dual resonance models}, Invent. Math. {\bf 62} (1980) 23--66.

A. Garsia and M. Haiman, {\em A graded representation model for Macdonald's polynomials}, Proc. Nat. Acad. USA {\bf 903} (1993) 3607--3610.

G.~Gonzalez-Sprinberg and J.-L.~Verdier, {\em Construction g\'eom\'etrique de la correspondance de McKay}, Ann. Sci. \'Ecole Norm. Sup. {\bf 16} (1983) 409--449.

L. G\"ottsche, {\em The Betti numbers of the Hilbert scheme of points on a smooth projective surface}, Math. Ann. {\bf 286} (1990) 193--207.

I.~Grojnowski, {\em Instantons and affine algebras I: the Hilbert scheme and vertex operators}, Math. Res. Lett. {\bf 3} (1996) 275--291.

M. Haiman, {\em Macdonald polynomials and Hilbert schemes}, UCSD preprint.


Y. Ito and I. Nakamura, {\em McKay correspondence and Hilbert schemes}, Proc. Japan Acad. Ser. {\bf A 72} (1996) 135--138.

M. Kapranov, {\em Chow quotients of Grassmannians}, in Gelfand Seminar {\bf 1} (eds. S.~Gelfand, S.~Gindikin), Adv. in Soviet Math. {\bf 16} (1993) 29--110, Amer. Math. Soc. Providence RI.


P.~Kronheimer, {\em The construction of ALE spaces as hyper-K\"ahler quotients}, J. Diff. Geom. {\bf 28} (1989) 665--683.

P.~Kronheimer and H.~Nakajima, {\em Yang-Mills instantons on ALE gravitational instantons}, Math. Ann. {\bf 288} (1990) 263--307. %

M. Lehn, %{\em Chern classes of tautological sheaves on Hilbert schemes of %points on surfaces}, Invent. Math. {\bf 136} (1999) 157--207.

I.~G. Macdonald, {\em Polynomial functors and wreath products}, J. Pure Appl. Alg. {\bf 18} (1980) 173--204.

J.~McKay, {\em Graphs, singularities and finite groups}, Proc. Sympos. Pure Math. {\bf 37}, Amer. Math. Soc, Providence, RI (1980) 183--186.

H. Nakajima, {\em Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras}, Duke Math. J. {\bf 76} (1994) 365--416.

H. Nakajima, {\em Heisenberg algebra and Hilbert schemes of points on projective surfaces}, Ann. Math. {\bf 145} (1997) 379--388.

H. Nakajima, {\em Lectures on Hilbert schemes of points on surfaces}, to be published by AMS.

H. Nakajima, {\em Quiver varieties and Kac-Moody algebras}, Duke Math. J. {\bf 91} (1998) 515--560.

H. Nakajima, {\em Private communications}.

I. Nakamura, {\em Hilbert schemes of abelian group orbits}, to appear in J. Alg. Geom.


S.-S. Roan, {\em Minimal resolutions of Gorenstein orbifolds in dimension three}. Topology 35 (1996) 489--508.

G.~Segal, {\em Unitary representations of some infinite dimensional groups}, Commun. Math. Phys. {\bf 80} (1981) 301--342.

G.~Segal, {\em Equivariant K-theory and symmetric products}, 1996 preprint (unpublished).


C. Vafa and E. Witten, {\em A strong coupling test of $S$-duality}, Nucl. Phys. {\bf B 431} (1994) 3--77.


H. Weyl, {\em The classical groups, their invariants and representations}, Princeton University Press, 1946.

A.~Zelevinsky, {\em Representations of finite classical groups. A Hopf algebra approach}, Lect. Notes in Math. {\bf 869}, Springer-Verlag, Berlin-New York, 1981.

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Latest revision as of 04:14, 17 September 2006

  

 R. Bezrukavnikov and V. Ginzburg, {\em Hilbert schemes and reductive groups}, in preparation.  



 J. Fogarty, {\em Algebraic families on an algebraic surface}, Amer. J. Math. {\bf 90} (1968) 511--521.  


 I.~B. Frenkel and V.~G. Kac, {\em Basic representations of affine Lie algebras and dual resonance models}, Invent. Math. {\bf 62} (1980) 23--66.  

 A. Garsia and M. Haiman, {\em A graded representation model for Macdonald's polynomials}, Proc. Nat. Acad. USA {\bf 903} (1993) 3607--3610.  

 G.~Gonzalez-Sprinberg and J.-L.~Verdier, {\em Construction g\'eom\'etrique de la correspondance de McKay}, Ann. Sci. \'Ecole Norm. Sup. {\bf 16} (1983) 409--449.  

 L. G\"ottsche, {\em The Betti numbers of the Hilbert scheme of points on a smooth projective surface}, Math. Ann. {\bf 286} (1990) 193--207.  

 I.~Grojnowski, {\em Instantons and affine algebras I: the Hilbert scheme and vertex operators}, Math. Res. Lett. {\bf 3} (1996) 275--291.  

 M. Haiman, {\em Macdonald polynomials and Hilbert schemes}, UCSD preprint.  


 Y. Ito and I. Nakamura, {\em McKay correspondence and Hilbert schemes}, Proc. Japan Acad. Ser. {\bf  A 72} (1996) 135--138.  

 M. Kapranov, {\em Chow quotients of Grassmannians}, in Gelfand Seminar {\bf 1} (eds. S.~Gelfand, S.~Gindikin), Adv. in Soviet Math. {\bf 16} (1993) 29--110, Amer. Math. Soc. Providence RI.  


 P.~Kronheimer, {\em The construction of ALE spaces as hyper-K\"ahler quotients}, J. Diff. Geom. {\bf 28} (1989) 665--683.  

 P.~Kronheimer and H.~Nakajima, {\em Yang-Mills instantons on ALE gravitational instantons}, Math. Ann. {\bf 288} (1990) 263--307.  %

 M. Lehn, %{\em Chern classes of tautological sheaves on Hilbert schemes of %points on surfaces}, Invent. Math. {\bf 136} (1999) 157--207.  

 I.~G. Macdonald, {\em Polynomial functors and wreath products}, J. Pure Appl. Alg. {\bf 18} (1980) 173--204.  

 J.~McKay, {\em Graphs, singularities and finite groups}, Proc. Sympos. Pure Math. {\bf 37}, Amer. Math. Soc, Providence, RI (1980) 183--186.  

 H. Nakajima, {\em Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras}, Duke Math. J. {\bf 76} (1994) 365--416.  

 H. Nakajima, {\em Heisenberg algebra and Hilbert schemes of points on projective surfaces}, Ann. Math. {\bf 145} (1997) 379--388.  

 H. Nakajima, {\em Lectures on Hilbert schemes of points on surfaces}, to be published by AMS.  

 H. Nakajima, {\em Quiver varieties and Kac-Moody algebras}, Duke Math. J. {\bf 91} (1998) 515--560.  

 H. Nakajima, {\em Private communications}.  

 I. Nakamura, {\em Hilbert schemes of abelian group orbits}, to appear in J. Alg. Geom.  


 S.-S. Roan, {\em Minimal resolutions of Gorenstein orbifolds in dimension three}. Topology 35 (1996) 489--508.  

 G.~Segal, {\em Unitary representations of some infinite dimensional groups}, Commun. Math. Phys. {\bf 80} (1981) 301--342.  

 G.~Segal, {\em Equivariant K-theory and symmetric products}, 1996 preprint (unpublished).  


 C. Vafa and E. Witten, {\em A strong coupling test of $S$-duality}, Nucl. Phys. {\bf B 431} (1994) 3--77.  


 H. Weyl, {\em The classical groups, their invariants and representations}, Princeton University Press, 1946.  

 A.~Zelevinsky, {\em Representations of finite classical groups. A Hopf algebra approach}, Lect. Notes in Math. {\bf 869}, Springer-Verlag, Berlin-New York, 1981.